Coverage and Capacity of Millimeter-Wave Cellular Networks

HEATH_LAYOUT_Layout 8/28/14 3:07 PM Page 70

MILLIMETER-WAVE COMMUNICATIONS FOR 5G

Coverage and Capacity of Millimeter-Wave Cellular Networks Tianyang Bai, Ahmed Alkhateeb, and Robert W. Heath, Jr.

ABSTRACT The millimeter-wave (mmWave) band offers the potential for high-bandwidth communication channels in cellular networks. It is not clear, however, whether both high data rates and coverage in terms of signal-to-noise-plus-interference ratio can be achieved in interferencelimited mmWave cellular networks due to the differences in propagation conditions and antenna topologies. This article shows that dense mmWave networks can achieve both higher data rates and comparable coverage relative to conventional microwave networks. Sum rate gains can be achieved using more advanced beamforming techniques that allow multiuser transmission. The insights are derived using a new theoretical network model that incorporates key characteristics of mmWave networks.

INTRODUCTION

The authors are with the University of Texas at Austin.

70

With advances in radio frequency (RF) circuits [1], the era of operating cellular networks in millimeter-wave (mmWave) bands is coming. Recent measurements have confirmed the feasibility of using mmWave as a cellular access channel [2]. While considered in wireless applications like backhaul, personal area networking, and wireless local area networks [3], the mmWave spectrum may be the key to providing an order of magnitude increase in the capacity of current cellular systems [4–6]. MmWave cellular systems will differ from conventional cellular systems due to the particular channel characteristics [2] and hardware constraints [7] at mmWave frequencies. System analysis of cellular networks needs to incorporate these features to provide a good characterization of coverage and capacity. There are several advantages in moving to the mmWave spectrum for cellular. First, the channel bandwidth available is likely to be much larger (e.g., 500 MHz per channel or more compared with 5–20 MHz in today’s microwave systems). Second, the small wavelength at mmWave frequencies makes it possible to pack a large number of antennas into the mmWave transceivers. With these large antenna arrays at both the base stations and mobile stations, mmWave systems can employ directional beamforming to boost the received signal power and

0163-6804/14/$25.00 © 2014 IEEE

reduce the impact of out-of-cell interference. The large number of antennas encourages the use of multiple-input multiple-output (MIMO) communication techniques to further enhance spectral efficiency. System simulations based on the measurement results have shown that dense mmWave networks can provide signal-to-noiseplus-interference ratio (SINR) coverage and spectrum efficiencies comparable to conventional microwave networks [5, 6]. Thus, the overall network capacity is expected to provide an order of magnitude gain in throughput given the large mmWave bandwidth. This article provides useful insights into the coverage and achievable rates of mmWave cellular networks. We show that due to particular features of the mmWave channel, mmWave systems generally will need high base station density to achieve acceptable coverage. Extremely dense mmWave networks will work in an interference-limited regime, where the management of interference will remain an important issue. To achieve high sum rates, mmWave base stations can serve multiple users simultaneously using multiuser MIMO techniques. Our results indicate that sophisticated beamforming techniques, such as hybrid beamforming [7], can further improve cell throughput by reducing intracell interference. More importantly, the comparable coverage in SINR can be translated into a significant gain in the achievable rate compared to microwave networks, as mmWave systems will potentially use much larger bandwidth. The results in this article were obtained using a new mathematical model for mmWave cellular systems. Important features of the model are the incorporation of random blockages and directional beamforming. The mathematical framework is developed based on our theoretical work on modeling random blockages in urban areas [8] and analyzing dense mmWave network performance using stochastic geometry [5, 9, 10]. Unlike the prior simulation-based approach [6], our model can be applied to different city environments, and is not limited by the few measurement results available. Our analytical framework also allows further analysis and optimization of mmWave performance, such as the asymptotic performance of extremely dense networks in [10]. The goal of this article is to expose the poten-

IEEE Communications Magazine • September 2014

HEATH_LAYOUT.qxp_Layout 8/28/14 1:16 PM Page 71

tial for high coverage and rate in mmWave cellular networks. First, we summarize distinguishing features of mmWave networks, such as channel characteristics and hardware constraints. Then we introduce models for two important features of mmWave cellular networks: blockage and beamforming. We present an introduction of a theoretical network model that incorporates these key mmWave features. Based on the analytical model, we illustrate the impact of base station density and different beamforming strategies on system performance. After that, we conclude with some highlights of future research directions.

CRITICAL ITEMS IN MMWAVE CELLULAR MmWave cellular networks are different from conventional networks in several ways. Large number of antennas: Antenna arrays will be used for directional beamforming in mmWave systems. Fortunately, realizing large arrays is possible due to the small wavelength at the mmWave frequencies. Directional beamforming at both transmitters and receivers provides not only large directivity gains to compensate for the high path loss, but also the capability to manipulate interference through more advanced beam shaping [7]. Sensitivity to blockages: MmWave signals are more sensitive to blockage effects than microwave, as certain materials, such as outer brick walls of buildings, cause severe penetration loss [4]. The isolation effects of walls make it hard for outdoor base stations to cover indoor users, which motivates the deployment of small cells and indoor distributed antennas. In general, blockages cause differences between unblocked or line-of-sight (LOS) paths and blocked or nonline-of-sight (NLOS) paths. Since diffraction effects are negligible, there are only a few scattering clusters [6]. In addition, mmWave signals suffer from foliage losses, which require a larger margin in the link budget for system design [2]. Variable propagation laws: MmWave signals will have weaker diffractions due to the small wavelength [4]. Thus, LOS signals will propagate as in free space. On the contrary, while reflections can establish NLOS communication links, even the best NLOS signals are shown to be much weaker than LOS signals [2]. This indicates a significant difference between LOS and NLOS path loss. For instance, measurements show that mmWave signals have an LOS path loss exponent close to 2, while the NLOS path losses are generally larger and more dependent on the scattering environment [2]. Sparsity in the channel: MmWave channels are sparse in terms of multipath components, as the number of significant scatterers tends to be smaller than microwave channels. For instance, measurements in New York City show that mmWave channels have only 2–3 clusters on average, the angles of arrival of which are located close to the boresight directions [6]. Furthermore, the angle spreads of reflected mmWave signals are small compared to microwave propagation. For example, the measurements in New

IEEE Communications Magazine • September 2014

York City indicate that 80 percent of the received signal angle spreads are less than 15° [6]. While this sparse nature of mmWave channels results in low-rank channel matrices, and hence has a negative impact on the large MIMO channel capacity, it can also be exploited to develop low-complexity channel estimation and precoding algorithms [7, 11]. Hardware constraints: MmWave transceivers are subject to a set of practical hardware constraints. For example, mixed signal components like analog-to-digital converters (ADCs) tend to be of higher power consumption and higher cost relative to microwave solutions. Hence, the traditional approach in microwave transceivers of dedicating a separate RF chain for each antenna is extremely difficult in mmWave systems. The analog phase shifters typically used in directional beamforming to beamsteer the transmitted signals are affected by a number of limitations as well. For instance, they can only change the phase of the transmitted signal, not the amplitude. Also, this phase can only vary within a finite set of quantized angles. These hardware constraints have a great impact on the transceiver architectures in mmWave systems [7].

We propose a stochastic model for blockages where a link is classified as either LOS or NLOS according to the LOS probability of the link. Based on the link classification, different propagation laws are applied to compute, for example, the received power.

MODELING BLOCKAGES A systematic study of network performance should incorporate the impact of blockages. One approach is to model them explicitly in terms of their sizes, locations, and orientations using geographic information system city data. While this can be performed using electromagnetic simulation tools like ray tracing and is well suited for simulations, it does not lead to elegant system analysis as in [12]. An alternative is to employ a stochastic building model where the building parameters are drawn randomly according to some distribution. The stochastic approach lends itself better to system analysis and can be applied to study system deployments under a variety of blockage parameters such as size and density. Random shape theory provides a concise way to model blockages as random distributed objects in space. One of the simplest object processes (a generalization of a point process) is the Boolean scheme [13], where the object centers form a Poisson point process (PPP), while each object is allowed to have independent shape, size, and orientation according to certain distributions. We used a Boolean scheme of rectangles to model blockages due to buildings in urban areas [8]. One interesting by-product was the derivation that the number of blockages on a link is a Poisson random variable the average of which scales with the link length. This allowed an important function of interest in mmWave systems to be computed: the probability that no blockages intersect the link, that is, the LOS probability of the link. We propose a stochastic model for blockages where a link is classified as either LOS or NLOS according to the LOS probability of the link. Based on the link classification, different propagation laws are applied to compute, for example, the received power. Note that because longer paths are more likely to be intersected by blockages, the LOS probability function is a (non-

71

HEATH_LAYOUT.qxp_Layout 8/28/14 1:16 PM Page 72

Equivalent LOS ball

NLOS link by reflections

Typical user

Indoor BS

NLOS BS

NLOS BS

LOS BSs Typical user

Directional beamforming LOS BS

Random blockage process (a)

(b)

Figure 1. MmWave cellular network model with random blockages: (a) the blockages modeled as a Boolean scheme of rectangles, with base stations distributed as a PPP. An outdoor base station can be either LOS or NLOS to the typical user at the origin; b) the model is simplified by treating close transmitters as LOS and further ones as NLOS. Equivalently, the irregular LOS region in a) is also approximated by a fixed ball in b).

increasing) function of the link length. Using the Boolean scheme of rectangles, the LOS probability function is a negative exponential function of the link length with decay rate that depends on the building perimeter and density. Other LOS probability functions have been proposed based on measurement results [6]. Note that the LOS probability of neighboring links may be correlated, as they might be blocked by the same buildings. Our first system-level analysis [8–10] though neglected this correlation, as we found that the error was relatively minor when evaluating the aggregated SINR coverage in the network [8]. Further simplifications of the blockage model are possible by approximating a general LOS function as a step function [9, 10]. Essentially, the LOS probability of the link is taken to be one within a certain fixed radius (e.g., determined through matching the first moment) and zero outside the radius. This approach is motivated by the observation that because of the exponentially decreasing LOS probability in [8], nearby links are likely to be LOS, while far links are likely to be NLOS. An interpretation is that the irregular geometry in Fig. 1a is replaced with the simplified structure in Fig. 1b. Such simplifications not only provide efficient expressions to compute SINR, but also enable simpler analysis of the network performance, as in the case of very dense networks [10]. Another issue resulting from blockages is the isolation of the indoor and outdoor environment in an mmWave network. Due to the high wall penetration loss with certain materials, indoor users are unlikely to be covered by an outdoor base station. Thus, indoor and outdoor users may be served by different tiers of base stations, and have different SINR and rate distribution in mmWave networks. Modeling buildings using the Boolean rectangle scheme makes it possible to differentiate indoor and outdoor environ-

72

ments in the analysis. For instance, when users are assumed to be uniformly distributed on the plane, the probability that a user is located indoors is simply the fraction of land covered by the random shapes. Conditioning on the relative locations of the user and base stations, different path loss formulas and user densities can be used to penalize the indoor-to-outdoor links and address the difference between indoor and outdoor scenarios. For the purpose of illustration, we focus on the performance analysis of outdoor users in this article, but the analysis can be generalized to also incorporate indoor-to-outdoor effects.

MODELING BEAMFORMING Directional beamforming is an essential component of mmWave systems since it provides array gains that can be used to overcome the high path loss and achieve sufficient link margins. Adaptive beamforming using large arrays for array gain distinguishes mmWave and microwave wireless systems. Hence, modeling beamforming in mmWave networks is critical for precise characterization of the network behavior and accurate evaluation of its performance. The main objective of adaptive beamforming is to shape the beam patterns (e.g., by beamsteering) so that the received signal-to-noise ration (SNR) is maximized. Full control of beam pattern shaping generally requires changing both the amplitude and phase of transmitted signals. The need for low-cost and low-power hardware, however, has pushed mmWave toward a simpler analog architecture that contains only digitally controlled constant modulus phase shifters. When simple maximum SNR beamsteering is assumed, it makes sense to approximate the actual array pattern by a sectored pattern where constant directivity gains are assumed for both the main lobe and side lobes to facilitate the

IEEE Communications Magazine • September 2014

HEATH_LAYOUT.qxp_Layout 8/28/14 1:16 PM Page 73

analysis. The approximation of sectored patterns makes it possible to characterize complex beamforming patterns with their key features: main lobe directivity gain, half-power beam width, and front-back ratio, as shown in Fig. 2. To have more degrees of freedom in designing the beamforming/precoding patterns, other mmWave-suitable precoding algorithms like hybrid precoding were proposed [7]. Hybrid precoding divides the required precoding processing between the analog and digital domains, and hence allows better control of the beam shape. The advantage of the joint analog/digital processing appears in multi-stream and multi-user transmission in which the additional digital precoding layer plays an important role in managing inter-stream and inter-user interference. Incorporating more complex beam patterns that arise from hybrid beamforming into the analysis is difficult because hybrid precoders are numerically solved by iterative algorithms [7] and do not have closed-form expressions. Hence, we compare hybrid beamforming with analog beamforming in simulations. In this article, we present simulations with both simple and more advanced beamforming strategies. For example, we present simulations for multi-user systems with each base station serving a number of users simultaneously. In this case, we assume that the base stations adopt hybrid precoding algorithms similar to [7] to approximate the performance of the unconstrained zero-forcing solution. The simulations illustrate the performance gain of hybrid precoders over analog-only beamsteering solutions when deployed in mmWave cellular systems.

A MATHEMATICAL MODEL FOR MMWAVE CELLULAR In this section, we review a theoretical model that incorporates blockages and beamforming in mmWave networks, leveraging concepts from stochastic geometry. The model is also validated by simulations using real scenario data. Stochastic geometry is an important tool to analyze large-scale networks [12]. In a stochastic geometry network model, tiers of base stations are modeled as independent point processes, mostly homogenous PPP. Each point in the point process represents a base station, and is endowed with other characteristics, such as the small-scale fading, antenna directivity gain, and transmit power of the base station, which are mathematically defined as the marks of the point process. Stochastic geometry enables the derivation of analytical expressions for performance metrics in large networks, which simplifies the network analysis and avoids the need for more extensive simulations. The model of PPP base stations generally provides a lower bound on the network performance in reality [12], as the base stations are randomly dropped without any planning. As shown in Fig. 1a, the mmWave network model consists of the following components. Blockage process: We use the random shape theory to model the random blockages as a stationary process of objects (e.g., the Boolean

IEEE Communications Magazine • September 2014

m

M θ

Figure 2. Approximating actual beamforming patterns with the sectored model. The sectored pattern captures key characteristics of the actual pattern, including the main lobe gain, half-power beam width, and front-back ratio.

scheme model used in [8]) on the plane. Based on the statistics of the blockage process, the LOS probability function of a link p(r) can be derived as a function of the link length r. We assume that p(r) is independent for all links and neglect correlation in the shadowing. The LOS probability function p(r) can be further simplified as a step function, as shown in Fig. 1b. Base station PPP: The base stations form a homogeneous PPP  on the same plane. Due to the presence of blockages, a base station can be located either indoors or outdoors. From the perspective of an outdoor user, the outdoor base stations can further be divided into two sub-processes: LOS and NLOS base stations. As the LOS probability for each base station is distance-dependent, the LOS and NLOS base stations form two non-homogeneous PPPs on the plane to which different path loss laws are applied. User PPP: The users form another independent PPP on the plane. We focus on the downlink performance of outdoor users in this article. Each user is assumed to be associated with the base station that has the smallest path loss. We further fix a typical user at the origin. By the stationarity of the blockage and base station processes, the performance of the typical user is representative of the aggregated downlink performance in the network [12]. Directional beamforming: We assume that directional beamforming is applied at both base stations and mobile stations. The typical user and its associated base station are assumed to have the perfect channel knowledge, and adjust their steering orientation perfectly to exploit the maximum directionality gain. The steering angles of the interfering base stations are randomly distributed. In the analysis, we approximate the actual array pattern by a sectored model, where constant directivity gains are assumed for the main lobe and the side lobe. We also examine the performance of sophisticated beamforming strategies using the actual array patterns in simulations because non-sectored patterns are less tractable to analyze. The spread of arrival angles would potentially

73

HEATH_LAYOUT.qxp_Layout 8/28/14 1:16 PM Page 74

1 0.9

SINR coverage probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

UT campus + 3GPP pattern Analytical model + sector pattern

0 -10

0

-5

5

10 15 20 SINR threshold (dB)

25

30

35

40

Figure 3. Comparison between the analytical model and the real building distribution on the campus of the University of Texas at Austin. The snapshot of the UT Austin campus is taken from Google Maps. creat a dependence on the received power as a function of the beamwidth, penalizing the narrow-beam antennas, and is not yet incorporated in the proposed analysis. In the simulations, we incorporate the impact of angle spread by using a clustered MIMO channel model, the parameters of which, like the distributions of the cluster number and the angle spread per cluster, are fitted to measurements [6]. Delay spreads from different clusters are not currently considered in the simulations, as few measurement results are available. Based on the system model, the downlink SINR in a mmWave network can be expressed as

SINR =

h0 G0 PL ( X0

)

σ 2 + ∑ l > 0:X l ∈Φ hl Gl PL ( X l

)

, (1)

where h l is the fading of signal power to the user, Gl is the combined gain of the transmitter and receiver beamforming, PL(◊) is the path loss to the user, s2 is the noise power, Xl denotes the location of the base stations, and X0 denotes the base station with the smallest path loss to the user. Note that different path loss formulae (e.g., different LOS and NLOS path loss exponent) will be used to compute the path loss PL(◊), given that the base station is LOS to the user or not. This applies to both the signal and interference terms. Efficient analytical expressions to compute the SINR distribution can be found in prior work [10].

UNDERSTANDING COVERAGE AND CAPACITY IN MMWAVE CELLULAR In this section, we provide insights on mmWave networks based on simulations of the SINR coverage probability and network capacity. We

74

assume the mmWave system is operated at 28 GHz with a bandwidth of 100 MHz (which conceivably could be much larger). The base stations are distributed according to a PPP with average cell radius Rc Note that a small average cell radius Rc indicates high base station density in the network. All base stations are assumed to have 30 dBm transmitting power, and the noise figure at the mobile stations is 7 dB. In terms of the blockage model, we apply the negative exponential LOS probability function derived in [8]. One key parameter of the blockage model is the average LOS range, which is defined as the average length of the LOS links in a network. Analysis in [8] also shows that the average LOS range scales inversely with the density and average size of the blockage process. We calculate the average LOS range as 224.5 m to match the real building distribution at the University of Texas at Austin (UT Austin), using Google Maps and the method proposed in [8]. We fit the following parameters to the channel measurements on the UT Austin campus: the LOS path loss exponent is 2.30, and the NLOS path loss exponent is 3.86 [2]. We also assume Nakagami fading with parameter 3 for NLOS links. Regarding the user distribution, we assume outdoor users also form another independent PPP on the plane and are associated with the base stations with the smallest path loss. Finally, we assume that the user PPP is 20 times denser than the base station PPP. The resource of a base station is assumed to be fairly shared between its associated users. First, we validate our proposed model by comparing with the simulations using a real building distribution on the UT Austin campus, where measurements in [2] were conducted. We observe most buildings are less than 150 m apart in this area. Thus, the average cell radius R c is assumed to be 50 m to guarantee that most outdoor users have access to LOS base stations. We only consider 2D beamforming in the azimuth

IEEE Communications Magazine • September 2014

HEATH_LAYOUT.qxp_Layout 8/28/14 1:16 PM Page 75

IEEE Communications Magazine • September 2014

1

SINR coverage probability

0.9

0.8

0.7

0.6

0.5

0.4

-5

Rc = 50 m Rc = 100 m Rc = 200 m Rc = 300 m 0

5 10 SINR threshold (dB)

15

20

Figure 4. SINR coverage probability with different average cell radii Rc.

1 0.9 0.8 Coverage probability

direction, and assume for the base station arrays that the main lobe gain is 20 dB, the beamwidth is 30°, and the FBR is 20 dB. Also, for the mobile station arrays, the main lobe gain is 10 dB, the beamwidth is 90°, and the FBR is 20 dB. In the real data simulation, we apply a modified version of the base station antenna pattern in [14] with smaller beam width, and assume that base stations can adjust their steering angle in space according to the user position. We find buildings cover 26.6 percent of the land in the snapshot, and the average building size there is 52 × 55 m2 [8]. Thus, using the method in [8, 10], the average LOS range in the analytical model is calculated as 224.5 m. In the analytical model simulation, we use the simplified sector model for the beamforming pattern. In Fig. 3, although there are some differences in the high SINR regime, the analytical model generally shows a close characterization of reality. Next, we show that mmWave can provide acceptable SINR coverage with high enough base station density. We plot the SINR coverage probability with different base station densities in Fig. 4, where we fix the LOS range as 224.5 m and change the base station density, that is, the average cell radius Rc in the network. Unlike the case of interference-limited microwave networks without blockages [12], the mmWave SINR coverage is sensitive to the base station density; high coverage probability is generally achieved in dense network cases. Comparing the curves for the 100-m cell radius and 50-m cell radius, increasing base station density in a sufficiently dense network, however, does not necessarily improve SINR coverage, as shown in Fig. 4. We present an intuitive explanation of the curves as follows. When increasing the base station density, coverage improves because the distance between the typical user and its associated base station becomes smaller, and it becomes more likely that a user can be served by a LOS base station. When the density is very high, however, a user sees more than one LOS base station and thus experiences significant interference. The results in Fig. 4 imply that sparse mmWave networks generally work in a power-limited regime, where coverage performance can be improved by increasing the base station density. The decrease of SINR coverage in the dense network regime indicates that dense mmWave networks may work in an interference-limited regime where coverage can be improved by better management of interference, such as base station cooperation or simply switching off some base stations. Now we compare the spectrum efficiency per served user, which is the rate achieved by the currently scheduled users with different multi user beamforming techniques. In the simulations, we assume that the base stations use 8 RF chains and uniform planar arrays of 8 × 8 antennas each, while the mobile stations use 4 RF chains and 4 × 4 uniform planar arrays. The baseline technique we simulate is conventional beamsteering, where base stations and mobile stations adjust their analog phase shifters to change steering angles of the arrays and maximize the directitivity gain in each link independently. In the hybrid precoding simulation, the

0.7 0.6 0.5 0.4 0.3 Single user–hybrid precoding Two users–hybrid precoding Three users–hybrid precoding Single user–beamsteering Two users–beamsteering Three users–beamsteering

0.2 0.1 0

0

10

5

15

Rate threshold (b/s/Hz)

Figure 5. Comparison of the spectrum efficiency per served user in multiuser mmWave systems. We assume that a user can receive multiple data streams in the hybrid beamforming case, while a single stream is transmitted in the beamsteering case.

precoders are built to approach the performance of zero-forcing unconstrained precoders. While showing that mmWave networks can apply directional beamforming to achieve high spectrum efficiency, the results in Fig. 5 also indicate that hybrid precoding is more robust to intracell interference compared to beamsteering, as the additional digital precoding layer provides higher capability of interference management. Although the spectrum efficiency per user is shown as a decreasing function of the number of users per cell, the results in Table 1 show that the sum cell throughput can be improved by applying multiuser beamforming.

75

HEATH_LAYOUT.qxp_Layout 8/28/14 1:16 PM Page 76

Transmission strategies

Average rate per served user

Average cell throughput

5% cell throughput

Micro SISO

31

31

1.2

Micro SU-MIMO

77.2

77.2

1.4

Micro massive MIMO

43.2

432.2

124.1

MmWave SU-Beamsteering

451.2

451.2

294.4

MmWave MU-beamsteering

450.9

901.7

576.0

MmWave MU-Hybrid

464.0

928.0

736.1

Table 1. Comparison of cell throughput in megabits per second.

Now we show that mmWave cellular can provide higher achievable rates than microwave networks. To make a fair comparison, we use the PPP network model to in all simulations, and assume that system overheads such as training data take up 20 percent of the total bandwidth. We also assume that all systems can at best support 64-quadrature amplitude modulation (QAM) as the highest order modulation. Thus, we clip the spectrum efficiency per data stream by 6 b/s/Hz. In the microwave networks, the downlink bandwidth is 20 MHz, and average cell radius is 200 m. The average rate per served user is the rate achieved by the users being served without penalizing the time-sharing factor. In the single-user (SU) MIMO microwave network, we assume base stations and mobile stations each have four antennas to perform spatial multiplexing with a zero-forcing precoder. In the massive MIMO simulations, we apply the asymptotic rate derived in [15], which upper bounds the achievable rate, and assume the base stations serve 10 users simultaneously. In the mmWave simulation, the average cell radius is 100 m. To compare different multiuser beamforming strategies, we assume that each of the base stations randomly chooses two users, and performs either beamsteering or hybrid beamforming to serve the users simultaneously. In the beamsteering simulation, the beams are steered independently, such that they might overlap and cause severe intra-cell interference. Simulation results in Table 1 show that with the large bandwidth at mmWave frequencies, mmWave systems outperform conventional microwave networks in terms of the achievable rate, and are promising to support 1 Gb/s transmission.

FUTURE RESEARCH DIRECTIONS We have established the promise of mmWave cellular for outdoor users in terms of coverage and capacity. Our results provide an important first step in establishing how and when mmWave works for outdoor cellular users. There are many potential areas for future research. Indoor coverage: Prior analyses mainly focus on the coverage of outdoor users. Indoor users

76

can be served by mmWave small cells, distributed antennas inside buildings, or base stations operating at lower carrier frequencies. It would be interesting to examine the performance of mmWave systems with indoor infrastructures colocated with buildings. Microwave-overlaid cells: MmWave systems will coexist with conventional microwave base stations. Microwave base stations can help cover the shadowed areas behind blockages and are more suitable to handle the control plane, as the microwave channels are more reliable and less sensitive to blockages. From a system analysis point of view, it is also of interest to incorporate overlaid microwave cells into the mmWave model and predict the performance of such multiband systems. User mobility: User mobility might be a critical issue in mmWave network design as the cell range is small and the antenna beam width is narrow. The effective rate of mobile users may suffer from the large amount of overhead due to frequent handovers and beam training. One promising solution is to switch highly mobile users to the microwave macrocells overlaid in the mmWave networks. Flexible user scheduling: The directional transmission scheme may allow more flexible user scheduling than in the conventional network. For instance, with narrow-beam antennas, a user can connect to a further available base station rather than waiting for a closer but occupied base station, with little interference to other users. This also indicates a change of methodology in the cellular network analysis: the serving regions of base stations may not follow from the Voronoi tessellation and can overlap each other. 3D system model: In reality, the heights of blockages, base station antennas, or even mobile users may have non-negligible impacts on system performance. Thus, it is of interest to incorporate the elevation height in analysis and extend the proposed framework into 3D space. A 3D system model will also make it possible to analyze the performance of the techniques that exploit the spatial degrees of freedom in elevation directions, such as 3D beamforming and vertical secterization.

CONCLUSIONS This article has shown that mmWave cellular networks have the potential for high coverage and capacity as long as the infrastructure is densely deployed. The basis for these conclusions is an analytical model for SINR that incorporates blockage, directional antennas, and co-channel interference. The analytical model has also been shown to be a good fit with reality. The impact of more sophisticated beamforming strategies has also been established, and it was found that hybrid beamforming leads to a notable improvement in sum rates. The analysis of mmWave systems offers many research opportunities, such as incorporating indoor infrastructure and microwave-overlaid cells, analyzing user mobility and user scheduling, and extending the system model to 3D space.

IEEE Communications Magazine • September 2014

HEATH_LAYOUT.qxp_Layout 8/28/14 1:16 PM Page 77

ACKNOWLEDGMENT This material is based on work supported in part by the National Science Foundation under Grants Nos. 1218338 and 1319556, and by a gift from Huawei Technologies, Inc.

REFERENCES [1] T. S. Rappaport et al., Millimeter Wave Wireless Communication, Prentice Hall, 2014. [2] T. Rappaport et al., “Millimeter Wave Mobile Communications for 5G Cellular: It Will Work!,” IEEE Access, vol. 1, 2013, pp. 335–49. [3] S. K. Yong and C.-C. Chong, “An Overview of Multigigabit Wireless Through Millimeter Wave Technology: Potentials and Technical Challenges,” EURASIP J. Wireless Commun., vol. 2007, pp. 1–10, 2006. [4] Z. Pi and F. Khan, “An Introduction to Millimeter-Wave Mobile Broadband Systems,” IEEE Commun. Mag., vol. 49, no. 6, June 2011, pp. 101–07. [5] S. Akoum, E. O. Ayach, and R. W. Heath Jr., “Coverage and Capacity in mmWave Cellular Systems,” Proc. 46th Asilomar Conf. Signals, Systems and Computers, 2012, pp. 688–92. [6] M. Riza Akdeniz et al., “Millimeter Wave Channel Modeling and Cellular Capacity Evaluation,” to appear, IEEE JSAC, 2014; http://arxiv.org/abs/1312.4921. [7] O. E. Ayach et al., “Spatially Sparse Precoding in Millimeter Wave MIMO Systems,” IEEE Trans. Wireless Commun., vol. 13, no. 3, Mar. 2014, pp. 1499–1513; http://arxiv.org/abs/1305.2460. [8] T. Bai, R. Vaze, and R. W. Heath Jr., “Analysis of Blockage Effects on Urban Cellular Networks,” IEEE Trans. Wireless Commun., June 2014, http://arxiv.org/abs/1309.4141. [9] T. Bai and R. W. Heath Jr., “Coverage in Dense Millimeter Wave Cellular Networks,” Proc. 47th Asilomar Conf. on Signals, Systems and Computers, Nov. 2013, pp. 1–5. [10] —, “Coverage and Rate Analysis for Millimeter Wave Cellular Networks,” submitted to IEEE Trans. Wireless Commun., Mar. 2014, http://arxiv.org/abs/1402.6430. [11] A. Alkhateeb et al., “Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems,” IEEE J. Selected Topics in Sig. Processing, arXiv preprint arXiv:1401.7426, 2013.

IEEE Communications Magazine • September 2014

[12] J. G. Andrews, F. Baccelli, and R. Krishna Ganti, “A Tractable Approach to Coverage and Rate in Cellular Networks,” IEEE Trans. Commun., vol. 59, no. 11, Nov. 2011, pp. 3122–34. [13] R. Cowan, “Objects Arranged Randomly in Space: An Accessible Theory,” Advances in Applied Probability, vol. 21, no. 3, 1989, pp. 543–69, http://www.jstor. org/stable/1427635. [14] 3GPP TR 36.942, “Evolved Universal Terrestrial Radio Access (E-UTRA); Radio Frequency (RF) System Scenarios (Release 11),” Mar. 2012. [15] T. Bai and R. W. Heath Jr., “Asymptotic Coverage Probability and Rate in Massive MIMO Networks,” submitted to IEEE Global Conf. Signal and Info. Processing, June 2014.

BIOGRAPHIES TIANYANG BAI ([email protected]) is a Ph.D. student in the Wireless Networking and Communication Group (WNCG) at the University of Texas at Austin (UT Austin). He received his B.Eng. degree from Harbin Institute of Technology, China, in 2011, and his M.S. degree from UT Austin in 2013, both in electrical engineering. His research interests include millimeter wave communications and applications of stochastic geometry.

The analysis of mmWave systems offers many research opportunities, such as incorporating indoor infrastructure and microwave-overlaid cells, analyzing user mobility and user scheduling, and extending the system model to 3D space.

AHMED ALKHATEEB ([email protected]) received his B.S. (with highest honors) and M.S. degrees from Cairo University, Egypt, in 2008 and 2012, respectively. He is currently a graduate student in WNCG in the Department of Electrical and Computer Engineering, at UT Austin. His research interests are in the broad area of network information theory, communication theory, and signal processing. In the context of wireless communication, his interests include cooperative communications, MIMO systems, and mmWave communication. ROBERT W. HEATH JR. [F’11] ([email protected]) is a Cullen Trust Endowed Professor in the Electrical and Communications Engineering Department at UT Austin and director of the WNCG. He received B.S. and M.S. degrees in electrical engineering from the University of Virginia and his Ph.D. in electrical engineering from Stanford University. He is the president and CEO of MIMO Wireless Inc. and chief innovation officer at Kuma Signals LLC. He is a registered Professional Engineer in Texas and an amateur radio operator.

77